Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 5x - 7$ and $ KL = 6x - 14$ Find $JL$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {5x - 7} = {6x - 14}$ Solve for $x$ $ -x = -7$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 5({7}) - 7$ $ KL = 6({7}) - 14$ $ JK = 35 - 7$ $ KL = 42 - 14$ $ JK = 28$ $ KL = 28$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {28} + {28}$ $ JL = 56$